How do you simplify the expression (sin^2tcot2^t)/(1-sin^2t)?

1 Answer
Apr 21, 2017

1

Explanation:

I'm guessing here (let me know if I'm wrong of course) that you meant

(sin^2(t)*cot^2(t))/(1-sin^2(t)), not (sin^2(t)*cot(2^t))/(1-sin^2(t))

If you meant the first one,

(sin^2(t)*cot^2(t))/(1-sin^2(t))

(NOTE: cot(x) = cos(x)/sin(x) by definition)

=(sin^2(t)*(\frac{cos^2(t)}{sin^2(t)}))/(1-sin^2(t))
=cos^2(t)/(1-sin^2(t))

(NOTE: use Pythagorean identity cos^2(x)+sin^2(x)=1)

=cos^2(t)/(cos^2(t))
=1

If not, it's a bit more tricky